Singapore Math: Place Value in Math in Focus

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1 Singapore Math: Place Value in Math in Focus There are several skills that are critical to mathematics success in the elementary grades. Among them are an understanding of number, number sense, and place value. Place value is the system of writing numerals in which the value of the digit is determined by its position, or relationship to the other digits. These values are multiples of a common base of 1 in our decimal system. In Singapore, where students consistently outperform American students in math, place value is considered a foundational skill for all mathematics learning. The U.S. edition of Singapore s math curriculum, Math in Focus, stresses mastery, coherence, and focus. Students master foundational math skills early and carry those skills with them as they progress through the grades. With each new concept learned, students build on what they have already learned. This systematic approach to mathematics is particularly evident in the program s approach to teaching place value. From grade level to grade level, place value is developed, honed, and applied to operations. As a result, numbers are demystified and students excel in mathematics because, for them, numbers become tools for solving problems rather than obstacles that cause frustration. Throughout Math in Focus, a concrete-pictorial-abstract approach encourages students to use place value blocks, chips, charts, and strips to create an association between the physical representation of numbers, the number symbol, and the number name, and later to perform arithmetic operations using these materials. These concrete and pictorial representations add meaning to numbers so that when students progress to the abstract, they have an understanding of what the numbers stand for. This way students experience problem solving as more than just a process, there is real meaning behind the elements of a problem. 1 Add. How many monkeys are there in all? 4 There are + = + = Chapter Addition Facts to 1 monkeys in all. You can add in any order. + = + 4 added on to is equal to. added on to also equal to. Grade 1A, Chapter, page is In Grade 1, place value is developed in a coherent, focused manner to stress the importance of the number 1 and help students master it. Grade 1, Chapter 1 begins with the study of the set of numbers from to 1. This is followed by an introduction to number bonds, showing the additive relationship between numbers less than 1 and, in later chapters, adding and subtracting up to 1. In these chapters, students come to understand 1 as an anchor number for future applications of sums and differences with 1 and multiples of 1.

2 Place value is introduced with numbers to 2, in a chapter that examines all teen numbers (11 to 19) as 1 plus numbers. This helps students master two major concepts that will play a pivotal role in their future mathematics learning: 1. Seeing all two-digit numbers as composed of tens and more 2. Understanding expanded notation or 1 ten plus 1, or one ten plus two,1 + or one ten plus three, and so on. In Grade 1, the study of place value concludes with the study of numbers to 1 with addition and subtraction. At this point, students are fully prepared to expand their understanding to three digits because of the gradual, strategic way in which it has been introduced, understood, and practiced. In addition, first-grade students are taught mental math in a chapter which calls on their knowledge of number bonds with 1 and multiples of 1 to solve mental computation problems. Next comes a chapter focused on practice with addition and subtraction to 2, which helps to solidify students understanding of 1 as an anchor number, the place value of numbers to 2, and adding and subtracting of numbers to 2. You can add tens mentally using the add the tens strategy. Find Group 2 into tens and ones. Step 1 Add the tens = Step 2 Add the result to the ones. + = So, =. 2 2 Make a 1. Then add = = Add mentally. 1 4 Find Group 1 into tens and ones.? Step 1 Add the tens. 1 + = Step 2 Add the result to the ones. + = So, =. Find Let s Practice 18 Chapter 14 Mental Math Strategies Make a 1. Then add. Grade 1B, Chapter 14, page = = = = = + = = on YoUR own Go to Workbook A: Practice 1, pages Lesson 1 Ways to Add 19 In Grade 2, students study how to count, read and write numbers up to 1,, and learn to add and subtract numbers to 1, with and without regrouping. Here place value is key to understanding why the algorithms work. Students learn how the place value ideas they learned in Grade 1 can be applied to the thousands place by using place value blocks. In addition, there is a chapter that teaches mental math strategies for adding and subtracting three-digit numbers without the use of paper and pencil. This solidifies students understanding of place value. Grade 1A, Chapter 8, page 19 using the add the tens strategy. Find Group 21 into tens, and hundreds and ones. learn You can add tens to a -digit number mentally 1 tens 2 By the second half of Grade 1, students using Math in Focus have developed a solid understanding of place value with numbers to 2. As the year progresses, the concept of place value continues to be developed with a chapter devoted to numbers to 4, followed by addition and subtraction to 4. In this chapter students begin their study of regrouping, which is clearly based on their earlier study of place value up to 4. Previously, students learned to make a ten and learned how to use number bonds. These foundational skills enable them to begin working with multi-digit numbers. Focusing only on numbers to 4 allows students to associate numerals with easily managed quantities of physical materials while the place value concept is developed. 21 hundreds 2 and ones Step 1 Add the tens. 1 + = 6 Step 2 Add the result to the hundreds = 26 and ones. So, 21 + = 26. Add mentally. 1 Find Group 1 into tens, and hundreds and ones. 1? 1 Step 1 Add the tens. + 4 = Step 2 Add the result to the hundreds and ones. 1 + = So, = = = 12 Chapter 1 Mental Math and Estimation Grade 2B, Chapter 1, page 12

3 In Grade, the place value chart is extended to the ten thousands place. Predictably, the study of addition and subtraction in the ten thousands place follows. The depth of development of place value in Grade directly correlates to the depth of development in Singapore Math. The chapter teaches the following skills: 1. Count, read, and write numbers to 1,. 2. Learn to count by ones, tens, hundreds, and thousands.. Show representations of numbers up to 1, using place value charts and place value strips. 4. Identify the place value of each digit in the number and express the number in standard, word, and expanded forms.. Compare and verbally describe sets of numbers using the terms least and greatest. 6. Write five-digit numbers in increasing or decreasing order.. Apply the number and place value concepts to identify and complete number patterns and find missing numbers on a number line. Throughout Math in Focus, students develop fluency in understanding numbers in multiple place value representations; for example, two thousand five hundred is 2 hundreds or 2 tens. In the later chapters of Grade, students explore strategies for mental math and addition and subtraction for numbers to 1,. These are the final chapters exploring place value addition and subtraction. In Grades 4 and, students continue to explore place value, but now with an emphasis on multiplication and division, and decimals. Hundreds Tens Ones Step Multiply the hundreds by. 2 hundreds 6 hundreds Total Multiplying with regrouping in hundreds, tens, and ones Find 12. How many are there? Find the missing numbers. Thousands Hundreds Tens Ones Step 1 Multiply the ones by. ones ones Regroup the ones. ones tens ones Step 2 Multiply the tens by. 2 tens 14 tens Add the tens. 14 tens 1 tens 1 tens Regroup the tens. 1 tens 1 hundred tens Step Multiply the hundreds by. 1 hundred hundreds Add the hundreds. hundreds 1 1 hundred 8 hundreds So, ,29 thousand hundreds tens ones 2 1, In 1,29, the digit is in the thousands place. it stands for. its value is. 2 Chapter Whole Number Multiplication and Division Grade 4A, Chapter, page 2 Find each missing number or word. Use base-ten blocks to help you. 4 In 2,48, the digit is in the hundreds place. the digit 4 stands for. the value of the digit 8 is. In 2,62, the values of the digit 2 are: 2, Chapter 1 Numbers to 1, Grade A, Chapter 1, page 14 In Grade 4, students extend their understanding of the place value system to the hundred thousands place and decimals to hundredths. Again, fluency with place value is emphasized as students learn to understand. For example, students see 8.2 as 8 and 2 tenths, or tens and 82 tenths, or 82 tenths, and can then apply their knowledge of place value to multiplication, division, and mental math. Express each of these as a decimal oz oz 2 6 in. in. 1 five hundredths 4 8 hundredths Find the decimals that the shaded parts represent. 6 Find the decimal for each point on the number line. Learn Find equivalent tenths and hundredths. Tenths Hundredths Tenths Hundredths 1 1 is equal to 1 1 or.1. 1 hundredths 1 tenth Yo u can regroup 1 hundredths as 1 tenth. 14 Chapter Decimals 4 Grade 4B, Chapter, page14

4 By Grade, students extend their understanding of the place value system to the millions place and the decimal places to thousandths. The focus is on division by two-digit numbers, decimal addition and subtraction, and multiplying and dividing decimals by whole numbers. As is the case throughout Math in Focus, place value is still the focus. For example, in learning how to multiply.6 by 8, students learn to think of the problem as multiplying 6 tenths by 8 to get 48 tenths, which is regrouped to form 4 and 8 tenths, or 4.8. Learn Divide decimals with one decimal place by a whole number with regrouping. Divide.8 by. Ones Tenths Step 1 Divide the ones by. ones ones. 8 Conclusion In Math in Focus place value is presented in a systematic and focused manner. From the very beginning students understand numbers as a system of tens. This system lays the foundation for all future lessons including computation skills, problem solving, the decimal system, and more. Mastery of math in the elementary grades is key for student success in the classroom and in the 21st century working world they will eventually enter. Since the 198s, students in Singapore have consistently outscored U.S. students in math. Now, with Math in Focus, U.S. students can learn using the same effective manner with which students in Singapore have had such success, preparing them for a lifetime of deep mathematics understanding and real-world problem solving. Step 2 Divide the tenths by. 8 tenths 1 tenth R tenths Regroup the remainder tenths. tenths hundredths Step Divide the hundredths by. hundredths 6 hundredths So, Lesson 9. Dividing Decimals Grade B, Chapter 9, page About the Author Patsy F. Kanter is an author, teacher, and international math consultant. She worked as the Lower School Math Coordinator and Assistant Principal at Isidore Newman School in New Orleans, Louisiana, for 1 years. Kanter is the author of a number of mathematics programs, including Afterschool Achievers: Math Club (K 8) and Summer Success : Math (K 8), and co-author of Every Day Counts : Calendar Math, Partner Games (K 6), and Practice Counts (1 6). She is a consulting author for Math in Focus, which is the U.S. version of Singapore s My Pals Are Here! Maths. Both programs are published by Marshall Cavendish, Singapore (part of Times Publishing Limited). 6

5 Houghton Mifflin Harcourt Publishing Company. All rights reserved. Printed in the U.S.A. 11/1 88 Z-148 Every Day Counts and Summer Success are registered trademarks of Houghton Mifflin Harcourt Publishing Company. Math in Focus is a trademark of Times Publishing Limited. Math in Focus: Singapore Math by Marshall Cavendish is the U.S. edition of My Pals are Here! Maths, the world-class program most widely used in Singapore classrooms today. Marshall Cavendish math programs have contributed to Singapore s consistent top performance on the Trends in International Math and Science Study (TIMSS) since hmheducation.com/mathinfocus